Previous noders have done an excellent job of explaining sleep paralysis but it seems that sufferers have differing experiences.
For example, a lot of people seem to experience hallucinations, out of body experiences or hear and feel things, whereas I have none of these. I simply wake up and can't move.
I started suffering from sleep paralysis about a year or so ago. My first experience was by far and away the worst. I woke up on my back unable to move with my tongue slipping down my throat until it started blocking my airway and I found it increasingly difficult to breath. Being fully conscious in my mind you can imagine how I felt at this point. Luckily I snapped out of it before the worst came to the worst. That was my introduction to sleep paralysis and after that I felt like the kids in Nightmare on Elm Street, terrified to go to sleep.
A couple of days ago I had double-sleep paralysis 3 mornings in a row. I term it this because it happened when I first woke up and I went through the process of snapping out of it, but then I went back to dozing, and it happened literally 10 seconds later again, very annoying.
It's not so frightening anymore as I have just learnt to lie there patiently until I snap out of it. Trying to move arms or legs simply feels like I'm pushing against a brick wall and after the effort I feel exhausted. I can wiggle my fingers and toes, but this doesn't seem to help to get out of it. I remember one time I did manage to move my hand up to my face and was trying to open my eyelids, but because my eyes were effectively paralysed and not working all I saw was a blur of colours.
If I had to give advice to sufferers, especially those who suffer symptoms similar to mine, I would say dont try and move, but learn to recognise when your mind and body have clicked back together, so when you do try to move, you can, and wont get as freaked out.